Deep Multi-Fidelity Active Learning of High-Dimensional Outputs

Shibo Li · Zheng Wang · Robert Kirby · Shandian Zhe


Many applications, such as in physical simulation and engineering design, demand we estimate functions with high-dimensional outputs. To reduce the expensive cost of generating training examples, we usually choose several fidelities to enable a cost/quality trade-off. In this paper, we consider the active learning task to automatically identify the fidelities and training inputs to query new examples so as to achieve the best learning benefit-cost ratio. To this end, we propose DMFAL, a Deep Multi-Fidelity Active Learning approach. We first develop a deep neural network-based multi-fidelity model for high-dimensional outputs, which can flexibly capture strong complex correlations across the outputs and fidelities to enhance the learning of the target function. We then propose a mutual information based acquisition function that extends the predictive entropy principle. To overcome the computational challenges caused by large output dimensions, we use the multi-variate delta method and moment-matching to estimate the output posterior, and Weinstein-Aronszajn identity to calculate and optimize the acquisition function. We show the advantage of our method in several applications of computational physics and engineering design. The code is available at

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